Question

A beam in Figure la is simply supported at A and C and subject to uniformly distributed load of 300 N/m with a moment of magnitude 2700 Nm. Express the shear and moment in terms of x and then sketch the shear and moment diagrams for the beam. 1.

Answer 1

the reaction at supports can be determined by considering moment equilibrium at support A and C

reaction at support A:

let us consider moment equilibrium about support C

2700-6*R_A=0

R_A=450 N(vertically upwards)

R_C=(300*6)-450=1350 N

From A to B:

Shear force =V(x)= R_A=450 N

Bending Moment diagram = M(x)=450*x

From B to C:

Shear force =V(x)= 450 - 300*(x-3)=1350-300x

Bending Moment = M(x)=450*x - 300*(x-3)²/2=450*x-150*(x-3)²

from C to D:

Shear Force=V(x)=450+1350-300*(x-3)=2700-300x

Bending moment=M(x)=450*x+1350*(x-6)-300*(x-3)²/2